$${\begin{align*} E &= \frac{\Delta m v_p^2}{2} \\&= \frac{1}{2} \frac{\Delta m (m_k g)^2 \Delta t}{\Delta m^2} \\&=\frac{1}{2} \frac{(m_kg)^2 \Delta t}{\Delta m} \end{align*}}$$